Conservation laws, modulation instability, and mixed semi‐rational solutions for a three‐component modified nonlinear Schrödinger equation

Abstract

In this paper, we study a three‐component modified nonlinear Schrödinger equation and main results include: (1) Lax pair and infinitely‐many conservation laws, (2) modulation instability of continuous waves, (3) semi‐rational solutions obtained through the Darboux transformation, and (4) four new types of mixed semi‐rational solutions provided for the three components , and .